Firstly, budget and quality are hugely correlated in the videogames industry. The reason is pretty simple. Firms will only be willing to have high budgets on games that are likely to make a return on that investment, which is more likely to occur if the game ends up being good. Therefore high potential games get high budgets and high budgets imply high production values. The result is a greater likelihood of making a higher quality game. There are of course exceptions to this and some developers have done amazing things with relatively small budgets, but these exceptions are few and far between.
Secondly, the budget issue is one of the primary reasons that the graphics vs gameplay issue is unbelievably ill-conceived. Graphics and gameplay have been positively correlated for each generation since gaming began. There are very few examples of games with awesome graphics relative to its peers that had awful gameplay, and at the same time there are very few examples of games with awful graphics relative to its peers that had fantastic gameplay. The graphics vs gameplay argument is quite simply silly in every possible way.
Bad graphics relative to its peers almost always implies bad gameplay, simply because bad graphics implies bad production values and there is no logical reason to believe that this wouldn't extend to the gameplay side of things. In fact it almost certainly would. The reverse is also true. Hence in terms of quality, gameplay and graphics tend to move together within any generation of gaming.
